{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:06Z","timestamp":1760242386502,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T00:00:00Z","timestamp":1496188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper is devoted to the semilocal convergence of a Househ\u00f6lder-like method for nonlinear equations. The method includes many of the studied third order iterative methods. In the present study, we use our new idea of restricted convergence domains leading to smaller    \u03b3   -parameters, which in turn lead to the following advantages over earlier works (and under the same computational cost): larger convergence domain; tighter error bounds on the distances involved, and at least as precise information on the location of the solution.<\/jats:p>","DOI":"10.3390\/a10020064","type":"journal-article","created":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T10:41:04Z","timestamp":1496227264000},"page":"64","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Expanding the Applicability of Some High Order Househ\u00f6lder-Like Methods"],"prefix":"10.3390","volume":"10","author":[{"given":"Sergio","family":"Amat","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica, Universidad Polit\u00e9cnica de Cartagena, Cartagena 30203, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9189-9298","authenticated-orcid":false,"given":"Ioannis","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Hern\u00e1ndez-Ver\u00f3n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Logro\u00f1o 26004, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0653-560X","authenticated-orcid":false,"given":"Natalia","family":"Romero","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Logro\u00f1o 26004, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1016\/j.amc.2006.11.127","article-title":"Construction of third-order modifications of Newton\u2019s method","volume":"189","author":"Chun","year":"2007","journal-title":"Appl. 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Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.amc.2008.08.050","article-title":"A modified Chebyshev\u2019s iterative method with at least sixth order of convergence","volume":"206","author":"Amat","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s12190-008-0065-0","article-title":"An inverse free Newton-Jarrat-type iterative method for solving equations under gamma condition","volume":"28","author":"Argyros","year":"2008","journal-title":"J. Appl. Math. Comput."},{"key":"ref_8","unstructured":"Kantorovich, L.V., and Akilov, G.P. (1982). Functional Analysis, Pergamon Press."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.cam.2013.10.054","article-title":"Expanding the applicability of Newton\u2019s method using Smale\u2019s theory","volume":"261","author":"Argyros","year":"2014","journal-title":"J. Appl. Math. 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